Symmetric difference
From Maths
(Unknown grade)
This page is a stub
This page is a stub, so it contains little or minimal information and is on a todo list for being expanded.The message provided is:
Find a ven diagram and make an infobox
(Unknown grade)
This page requires references, it is on a todo list for being expanded with them.
Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.
Contents
Definition
Let [ilmath]A,B\in\mathcal{P}(X)[/ilmath] be two subsets of a set [ilmath]X[/ilmath]. We define the symmetric difference of [ilmath]A[/ilmath] and [ilmath]B[/ilmath] as^{[1]}:
 [ilmath]A\triangle B:=(AB)\cup(BA)[/ilmath]^{[Note 1]}
 In words: [ilmath]A\triangle B[/ilmath] contains (everything in [ilmath]A[/ilmath] and not in [ilmath]B[/ilmath]) and (everything in [ilmath]B[/ilmath] but not in [ilmath]A[/ilmath]).
Claim 1: this is equivalent to [ilmath]A\triangle B:=(A\cap B^C)\cup(A^C\cap B)[/ilmath]^{[1]}
Proof of claims
(Unknown grade)
This page requires one or more proofs to be filled in, it is on a todo list for being expanded with them.
Please note that this does not mean the content is unreliable. Unless there are any caveats mentioned below the statement comes from a reliable source. As always, Warnings and limitations will be clearly shown and possibly highlighted if very important (see template:Caution et al).
The message provided is:
The message provided is:
Trivial, be bothered to show this
Notes
 ↑ Here [ilmath]AB[/ilmath] denotes set subtraction.
References
 ↑ ^{1.0} ^{1.1} Measure Theory  Paul R. Halmos
